(ii). Let the initial volume of air in a cylinder be V lit. In each stroke, the vacuum pump removes ¼ of air remaining in the cylinder at a time. In other words, after every stroke, only 1-¼ = ¾th part of air will remain.

Therefore, volumes will be V, (3v/4), (3v/4)², (3v/4)³…

Clearly, it can be observed that the adjacent terms of this series do not have the same difference between them. Therefore, this is not an A.P.

(iii). Cost of digging for first meter = 150

Cost of digging for first 2 meter = 150 + 50 = 200

Cost of digging for first 3 meters = 200 + 50 = 250

Cost of digging for first 4 metres = 250 + 50 = 300

Clearly, 150, 200, 250, 300 … forms an A.P. because every term is 50 more than the preceding term.

(iv). We know that if Rs P is deposited at r% compound interest per annum for n years, our money will be [1 + (r/100)]n after n years.